help with null claim

The question is this... Test the claim about the population mean at the given level of significance using the given sample statistics.

Claim mean> 1030; a = 0.05, sample statistics (xbar) = 1035, s= 23 n = 35. This is what I have and I'm wondering if I have it right. I assumed it was a right tail test with the z test with z(little o) = 1.644. and do not reject the null hypothesis. Does this sound close?

The question is this... Test the claim about the population mean at the given level of significance using the given sample statistics.

Claim mean> 1030; a = 0.05, sample statistics (xbar) = 1035, s= 23 n = 35. This is what I have and I'm wondering if I have it right. I assumed it was a right tail test with the z test with z(little o) = 1.644. and do not reject the null hypothesis. Does this sound close?

As the sample size is small, and you are working with the sample SD, you
should be using the t-test, with 34 degrees of freedom.